I am using the Steam version of The Cave on Windows 7 x64.
I have a PS2 controller to USB converter Throughout the whole game, it called the currently selected character P2, I think because it always calls the keyboard P1, even though you don't seem to be able to control them simultaneously.
On my first two play-throughs with my USB controller everything went fine, until I climbed up the final ladder with 2 characters. After that the game refused to move the final character with the controller. It was still receiving input from the controller because I could use it to go to the menu, but couldn't move the character with it. I was able to finish though, because keyboard control worked.
On my third play-through, I noticed the P2 controller issue, and thought that perhaps I had the controller plugged in the wrong port, and switched it part way through. Turns out that the other port is P3, and for the rest of the game I had a P3 somewhere on the player selection.
When I got to the end this time, I'm entirely unable to move the 3rd and final character, I've tried the controller in the P2 port, in the P3 port, and the keyboard, and even tried mouse movement but that never seemed to work for me. I saved and exited and got back in, and still nothing will move that last character, even though it's receiving input from everything enough to go into the menus, move the cursor, highlight items, etc.